higgs production in the .9plus.9minus.910.95.9mssm: … · 2017. 6. 6. ·...
TRANSCRIPT
Higgs production in the MSSM:Transverse momentum resummation
Marius Wiesemann
University of Zürich
HP2 : High Precision for Hard Processes, Florence (Italy)
3-5 August, 2014
Outline
1. Transverse momentum resummation
2. SM vs. MSSM Higgs production
3. bb̄H: NNLO+NNLL distribution in the 5FS
4. Gluon fusion: NLO+NLL distribution in the MSSM
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 1 / 23
pT resummationI production of colorless particle (mass M)I problem: pT distribution diverges at pT → 0I reason: large logs ln p2
T/M2 for pT � M
αs : ln(p2T/M2), ln2(p2
T/M2)
α2s : ln(p2T/M2), ln2(p2
T/M2), ln3(p2T/M2), ln4(p2
T/M2)
· · ·
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 23
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pT resummationI production of colorless particle (mass M)I problem: pT distribution diverges at pT → 0I reason: large logs ln p2
T/M2 for pT � M
αs : ln(p2T/M2), ln2(p2
T/M2)
α2s : ln(p2T/M2), ln2(p2
T/M2), ln3(p2T/M2), ln4(p2
T/M2)
· · ·I solution: all order resummation
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 23
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Transverse momentum resummationI developed already 30 years ago
[Parisi, Petronzio ’79], [Dokshitzer, Diakonov, Troian ’80], [Curci, Greco, Srivastava
’79], [Bassetto, Ciafaloni, Marchesini ’80], [Kodaira, Trentadue ’82], [Collins, Soper,
Sterman ’85]
dσ(res)Ndp2
T∼∫
db b2 J0(b pT ) S(b,A,B)HN fN fN , HN = HN CN CN
I we use newer formulation including various improvements:[Catani, de Florian, Grazzini ’01], [Bozzi, Catani, de Florian, Grazzini ’06]
I H embodies whole process dependenceI L = ln(Q2 b2/b2
0)→ L′ = ln(Q2 b2/b20 + 1)
→ reduction of impact at high pT (low b)→ unitarity constraint
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 3 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
+
[dσ(res)
dp2T
]l.a.
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI matched (resummed) cross section:[
dσdp2
T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
+
[dσ(res)
dp2T
]l.a.
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23
MatchingI unitarity (due to L→ L′):∫
dp2T
[dσ
dp2T
]f.o.+l.a.
≡[σ(tot)
]f.o..
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 5 / 23
ApplicationsI SM Higgs production through gluon fusion (heavy-top limit)
[Bozzi, Catani, de Florian, Grazzini ’06]
I Slepton pair production[Bozzi, Fuks, Klasen ’06]
I Vector boson pair production: WW and ZZ[Grazzini ’06], [Grazzini, Frederix ’08]
I Drell-Yan[Bozzi, Catani, Ferrera, de Florian, Grazzini ’10]
I SM Higgs production through gluon fusion with full massdependence[Mantler, MW ’12], [Grazzini, Sargsyan ’13]
I Recently: Higgs production through bottom annihilation[Harlander, Tripathi, MW ’14]
I new: MSSM Higgs production in gluon fusion[Harlander, Mantler, MW ’14]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 6 / 23
ApplicationsI SM Higgs production through gluon fusion (heavy-top limit)
[Bozzi, Catani, de Florian, Grazzini ’06]
I Slepton pair production[Bozzi, Fuks, Klasen ’06]
I Vector boson pair production: WW and ZZ[Grazzini ’06], [Grazzini, Frederix ’08]
I Drell-Yan[Bozzi, Catani, Ferrera, de Florian, Grazzini ’10]
I SM Higgs production through gluon fusion with full massdependence[Mantler, MW ’12], [Grazzini, Sargsyan ’13]
I Recently: Higgs production through bottom annihilation[Harlander, Tripathi, MW ’14]
I new: MSSM Higgs production in gluon fusion[Harlander, Mantler, MW ’14]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 6 / 23
1. Transverse momentum resummation
2. SM vs. MSSM Higgs production
3. bb̄H: NNLO+NNLL distribution in the 5FS
4. Gluon fusion: NLO+NLL distribution in the MSSM
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 7 / 23
SM vs. MSSM Higgs production
[TeV]s7 8 9 10 20 30 40 50 60 70 80 210
[pb]
m
-210
-110
1
10
210
310
LHC
HIG
GS
XS W
G 2
014
H (NNLO+NNLL QCD + NLO EW)
App
H (NNLO QCD)
q qApp
WH (NNLO QCD)
App ZH (NNLO QCD)
App
H (NLO QCD)
t tApp HH (NLO QCD)
App
H (NNLO QCD - 5FS)
b bApp
= 125 GeVHMMSTW2008
I SM:I gluon fusion by far
dominantI bb̄H sizeable only with
b-tagging
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 23
SM vs. MSSM Higgs production
[TeV]s7 8 9 10 20 30 40 50 60 70 80 210
[pb]
m
-210
-110
1
10
210
310
LHC
HIG
GS
XS W
G 2
014
H (NNLO+NNLL QCD + NLO EW)
App
H (NNLO QCD)
q qApp
WH (NNLO QCD)
App ZH (NNLO QCD)
App
H (NLO QCD)
t tApp HH (NLO QCD)
App
H (NNLO QCD - 5FS)
b bApp
= 125 GeVHMMSTW2008
I SM:I gluon fusion by far
dominantI bb̄H sizeable only with
b-tagging
I MSSM/2HDM:I 3 neutral Higgs: h, H and AI yb/yt enhanced by tanβI h: constrained to be SM-likeI bb̄H/A dominant for large tanβ
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 23
Associated H(bb̄) production4-flavour scheme
I exclusive up to NLO[Dittmaier, Krämer, Spira ’04]
[Dawson, Jackson, Reina, Wackeroth ’04]
5-flavour scheme
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 23
Associated H(bb̄) production4-flavour scheme
I exclusive up to NLO[Dittmaier, Krämer, Spira ’04]
[Dawson, Jackson, Reina, Wackeroth ’04]
5-flavour scheme
I inclusive up to NNLO[Harlander, Kilgore ’03]
I exclusive up to NNLO[Buehler, Herzog, Lazopoulos,
Mueller ’12]
I NLO+NLL pT resummation[Belyaev, Nadolsky, Yuan ’06]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 23
1. Transverse momentum resummation
2. SM vs. MSSM Higgs production
3. bb̄H: NNLO+NNLL distribution in the 5FS
4. Gluon fusion: NLO+NLL distribution in the MSSM
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 10 / 23
bb̄H : Ingredients of the calculation[dσ
dp2T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.
I analytic pT -distribution [Ozeren ’10]
I resummation coefficients from Drell-YanA(1), A(2), B(1) [Kodaira, Trentadue ’82],C (1) [Davies, Stirling ’84],A(3) [Becher, Neubert ’11],C (2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23
αs : b b
α2s : b b b b
bb̄H : Ingredients of the calculation[dσ
dp2T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
I analytic pT -distribution [Ozeren ’10]
I resummation coefficients from Drell-YanA(1), A(2), B(1) [Kodaira, Trentadue ’82],C (1) [Davies, Stirling ’84],A(3) [Becher, Neubert ’11],C (2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23
bb̄H : Ingredients of the calculation[dσ
dp2T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
I analytic pT -distribution [Ozeren ’10]
I resummation coefficients from Drell-YanA(1), A(2), B(1) [Kodaira, Trentadue ’82],C (1) [Davies, Stirling ’84],A(3) [Becher, Neubert ’11],C (2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]
I Hbb̄H(1) = 3CFI new: [Harlander, Tripathi, MW ’14]
Hbb̄H(2) = 10.47± 0.08 (numerical result)
Hbb̄H(2) = CF
[ (32164 −
1348π
2)
CF +(−365
288 + π2
12
)Nf
+(5269576 −
512π
2 − 94ζ3)
CA
]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23
from universal form of H(2) [Catani, Cieri, de Florian, Grazzini ’13]
→ see Leandro’s talk
b
b
bb̄H : Ingredients of the calculation[dσ
dp2T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
I analytic pT -distribution [Ozeren ’10]
I resummation coefficients from Drell-YanA(1), A(2), B(1) [Kodaira, Trentadue ’82],C (1) [Davies, Stirling ’84],A(3) [Becher, Neubert ’11],C (2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]
I Hbb̄H(1) = 3CFI new: [Harlander, Tripathi, MW ’14]
Hbb̄H(2) = 10.47± 0.08 (numerical result)
Hbb̄H(2) = CF
[ (32164 −
1348π
2)
CF +(−365
288 + π2
12
)Nf
+(5269576 −
512π
2 − 94ζ3)
CA
]= 10.52 . . .
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23
from universal form of H(2) [Catani, Cieri, de Florian, Grazzini ’13]
→ see Leandro’s talk
b
b
bb̄H : Ingredients of the calculation[dσ
dp2T
]f.o.+l.a.
=
[dσ
dp2T
]f.o.−[
dσ(res)
dp2T
]f.o.
+
[dσ(res)
dp2T
]l.a.
I analytic pT -distribution [Ozeren ’10]
I resummation coefficients from Drell-YanA(1), A(2), B(1) [Kodaira, Trentadue ’82],C (1) [Davies, Stirling ’84],A(3) [Becher, Neubert ’11],C (2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]
I + Hbb̄H(1) and Hbb̄H(2)
I third term: modified version of HqT
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23
[Bozzi, Catani, de Florian, Grazzini ’03 ’05]
[de Florian, Ferrera, Grazzini, Tommasini ’11]
bb̄H : ChecksI analytic pT -distribution checked against numerical H + jet
calculation at NLO [Harlander, Ozeren, MW ’10]
I unitarity:∫ dσ
dpTdpT = total
I for various µF , µR valuesI integral Qres-independent
I fixed order (pT → 0) = logs (pT → 0)I for various µF , µR valuesI independent of Qres
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 12 / 23
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bb̄H : ResultsNLO+NLL distribution:[Harlander, Tripathi, MW ’14], [Belyaev, Nadolsky, Yuan ’06][
dσdp2
T
]NLO+NLL
=
[dσ
dp2T
]NLO−[
dσ(res)dp2
T
]NLO
+
[dσ(res)dp2
T
]NLL
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 13 / 23
Q = mH/2 Q = mH/4
bb̄H : ResultsNLO+NLL distribution:[Harlander, Tripathi, MW ’14], [Belyaev, Nadolsky, Yuan ’06][
dσdp2
T
]NLO+NLL
=
[dσ
dp2T
]NLO−[
dσ(res)dp2
T
]NLO
+
[dσ(res)dp2
T
]NLL
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 13 / 23
higher order effect! [Banfi, Monni, Zanderighi ’13]
Q = mH/2 Q = mH/4
bb̄H : ResultsNNLO+NNLL distribution:[Harlander, Tripathi, MW ’14][
dσdp2
T
]NNLO+NNLL
=
[dσ
dp2T
]NNLO
−[
dσ(res)dp2
T
]NNLO
+
[dσ(res)dp2
T
]NNLL
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 14 / 23
Q = mH/4
bb̄H : ResultsScale uncertainties:[Harlander, Tripathi, MW ’14][
dσdp2
T
]NNLO+NNLL
=
[dσ
dp2T
]NNLO
−[
dσ(res)dp2
T
]NNLO
+
[dσ(res)dp2
T
]NNLL
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 15 / 23
Q-variation Q+µF+µR -variation
bb̄H : ResultsComparison to 5FS NLO+PS:[Frederix, Frixione, Maltoni, Torielli, MW]
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 16 / 23
Preliminary
analytic resum:µF = µR = mT/4
NLO+PS:µF = µR = HT/4
bb̄H : ResultsComparison to 4FS NLO+PS:[Frederix, Frixione, Maltoni, Torielli, MW]
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 17 / 23
Preliminary
analytic resum:µF = µR = mT/4
NLO+PS:µF = µR = HT/4
bb̄H : ResultsComparison to 4FS NLO+PS:[Frederix, Frixione, Maltoni, Torielli, MW]
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 17 / 23
Preliminary
→ Qshowersignificantly lowerthan Higgs mass(peak around 45 GeV, similar to µF )(default shower scalein MG5_aMCdistribution peaksaround 190 GeV)
analytic resum:µF = µR = mT/4
NLO+PS:µF = µR = HT/4
1. Transverse momentum resummation
2. SM vs. MSSM Higgs production
3. bb̄H: NNLO+NNLL distribution in the 5FS
4. Gluon fusion: NLO+NLL distribution in the MSSM
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 18 / 23
Gluon fusion: Ingredients of the calculationI NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05]
I MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)
dσ
dpT=
dσf.o.
dpT− dσlogs
dpT+
dσres
dpT
H
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23
Gluon fusion: Ingredients of the calculationI NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05]
I MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)
dσ
dpT=
dσf.o.
dpT− dσlogs
dpT+
dσres
dpT
H
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23
Amplitudes from SusHi[Harlander, Liebler, Mantler ’12]
Gluon fusion: Ingredients of the calculationI NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05]
I MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)
dσ
dpT=
dσf.o.
dpT− dσlogs
dpT+
dσres
dpT
H
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23
σ(0)t+b
Amplitudes from SusHi[Harlander, Liebler, Mantler ’12]
Gluon fusion: Ingredients of the calculationI NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05]
I MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)
dσ
dpT=
dσf.o.
dpT− dσlogs
dpT+
dσres
dpTH
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23
, etc.
σ(0)t+b
φ φAmplitudes from SusHi[Harlander, Liebler, Mantler ’12]
Gluon Fusion: ResultsNLO+NLL ratio in the MSSM/SM (light Higgs):[Harlander, Mantler, MW ’14]
RS(pT ) = dσS/dpTdσSM/dpT
NS(pT ) = dσS/dpTdσSM/dpT
· σSMσS
0.9
0.92
0.94
0.96
0.98
1
0 50 100 150 200 250 300
RS(p
T)
pT [GeV]
pp @ 13 TeV
tauphobic(800,16)tauphobic(800,29.5)
mhmax(300,6.5)mhmodp(500,17)
mhmodm(500,16.5)lightstau(500,12)
0.9
0.92
0.94
0.96
0.98
1
0 50 100 150 200 250 300
RS(p
T)
pT [GeV]
pp @ 13 TeV
0.96
0.98
1
1.02
1.04
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
tauphobic(800,16)tauphobic(800,29.5)
mhmax(300,6.5)mhmodp(500,17)
mhmodm(500,16.5)lightstau(500,12)
0.96
0.98
1
1.02
1.04
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 20 / 23
ratio to SM shape-ratio to SM
Benchmark Scenarios from [Carena, Heinemeyer, Stål, Wagner, Weiglein ’13]
light Higgs light Higgs
Gluon Fusion: Results
10-7
10-6
10-5
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT
tauphobic, mA = 800 GeV
tan(β) = 16tan(β) = 29.5
10-6
10-5
10-4
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT
tauphobic, mA = 800 GeV
tan(β) = 16tan(β) = 29.5
10-7
10-6
10-5
10-4
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT
mhmodm, mA = 800 GeV
tan(β) = 17tan(β) = 40
10-7
10-6
10-5
10-4
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT [GeV]
10-6
10-5
10-4
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT
mhmodm, mA = 800 GeV
tan(β) = 17tan(β) = 40
10-6
10-5
10-4
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT [GeV]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 21 / 23
heavy Higgs pseudo-scalar
heavy Higgs pseudo-scalar
Gluon Fusion: ResultsNLO+NLL distribution in the MSSM (left: heavy, right: pseudo-scalar):[Harlander, Mantler, MW ’14]
NS(pT ) = dσS/dpTdσSM/dpT
· σSMσS
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
tauphobic(800,16)tauphobic(800,29.5)
mhmodp(800,17)mhmodp(800,40)
mhmodm(800,16.5)mhmodm(800,40)
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
tauphobic(800,16)tauphobic(800,29.5)
mhmodp(800,17)mhmodp(800,40)
mhmodm(800,16.5)mhmodm(800,40)
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0 50 100 150 200 250 300
NS(p
T)
pT [GeV]
pp @ 13 TeV
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 22 / 23
heavy Higgs pseudo-scalar
Conclusions and OutlookConclusions:
I bb̄H and gluon fusion crucial in MSSM/2HDMbb̄H:
I missing hard coefficient at two-loop for H(bb̄) determinedI first calculation of NNLL pT -effects for H(bb̄) productionI strong reduction of resummation scale dependenceI consistent with NLO+PS resultsI remarkable agreement of 5FS NNLO+NNLL with 4FS NLO+PS
gluon fusion:I MoRe-SusHi: MSSM effects included in analytic resummationI h: quite SM-likeI H/A: significant shape/normalization distortion from b-loop
Outlook:I first NLO+PS in 4FSI complete differential comparison 4FS and 5FS for H(bb̄)I inclusion of bb̄H into MoRe-SusHi
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 23 / 23
BackUp
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 1 / 11
Resummation coefficients: determination of Hbb̄H,(2)b
I hard-collinear function:
Hbb̄H(2)
bb̄←bb̄(z) = Hbb̄H(2)b δ(1− z) + known
I use unitarity:
[σ̂(tot)bb̄
]f.o.
=
∫dp2
T
[
dσbb̄dp2
T
]f.o.−
dσ(res)bb̄dp2
T
f.o.
+
∫dp2
T
dσ(res)bb̄dp2
T
l.a.︸ ︷︷ ︸
=z σ̂(0)
bb̄ Hbb̄H(2)
bb̄←bb̄
→ numerical result: Hbb̄H,(2)b = 10.47± 0.08
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 11
[Catani, Cieri, de Florian,
Ferrera, Grazzini ’12]
Resummation coefficients: determination of Hbb̄H,(2)b
I hard-collinear function:
Hbb̄H(2)
bb̄←bb̄(z) = Hbb̄H(2)b δ(1− z) + known
I use unitarity:
[σ̂(tot)bb̄
]f.o.
=
∫dp2
T
[
dσbb̄dp2
T
]f.o.−
dσ(res)bb̄dp2
T
f.o.
+
∫dp2
T
dσ(res)bb̄dp2
T
l.a.︸ ︷︷ ︸
=z σ̂(0)
bb̄ Hbb̄H(2)
bb̄←bb̄
→ numerical result: Hbb̄H,(2)b = 10.47± 0.08
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 11
[Catani, Cieri, de Florian,
Ferrera, Grazzini ’12]
Resummation coefficients: determination of Hbb̄H,(2)b
→ numerical result: Hbb̄H,(2)b = 10.47± 0.08
I recently: universal Form of H(2) determined[Catani, Cieri, de Florian, Grazzini ’13]
→ for both gg- and qq̄-initiated processes→ process dependence: finite part of virtuals
I anlytical result from two-loop virtuals:[Harlander, Tripathi, MW ’14]
Hbb̄H,(2)b = CF
[(32164 −
1348π
2)
CF +
(−365288 +
π2
12
)Nf
+
(5269576 −
512π
2 − 94ζ3
)CA
]= 10.52 . . .
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 3 / 11
ResultsPDF+αs uncertainties:[Harlander, Tripathi, MW ’14]
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 11
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bb̄H : ResultsQ = mH/2 vs. Q = mH/4:[Harlander, Tripathi, MW ’14][
dσdp2
T
]NNLO+NNLL
=
[dσ
dp2T
]NNLO
−[
dσ(res)dp2
T
]NNLO
+
[dσ(res)dp2
T
]NNLL
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M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 5 / 11
pT resummationI determination of resummation coefficients:
I expand resummation formula in αsI compare to small pT region of fixed order cross sectionI Q0 � M:
αs :
∫ Q20
0
[dσ(res)
dp2T
]NLO
dp2T
!=
∫ Q20
0
[dσ
dp2T
]NLO
dp2T
f (A(1),B(1),C (1),H(1)) = K2 ln2(Q20/M2) + K1 ln(Q2
0/M2) + K0
+O(Q20/M2)
I known for Drell-Yan and gg → H up to NNLL[Kodaira, Trentadue ’82], [Davies, Stirling ’84], [Catani, D’Emilio, Trentadue ’88],
[de Florian, Grazzini ’01], [Becher, Neubert ’11], [Catani, Grazzini ’11], [Catani,
Cieri, de Florian, Ferrera, Grazzini ’12]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 6 / 11
Gluon fusion: Choosing the resummation scaleI Qb ≡ Qtb = mb in SM suggested due to appearance of terms
[Grazzini, Sargsyan ’13]
∼ ln(mb/pT )
I vanish as pT → 0⇒ no factorization breaking, no Sudakov logsI directly related to ln(mb/mH) in total rateI HOWEVER: could spoil collinear/soft approximation⇒ Sudakov resummation would be unsufficient
I BUT: if small, treated as all other finite terms (powercorrections in pT )
I choosing Qb (and Qtb) – 2 proposals:1. analyze size of finite terms
[Banfi, Monni, Zanderighi ’13]2. consider validity of collinear/soft approximation
[Bagnaschi, Vicini]
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 7 / 11
When quark masses are taken into account, new non-factorizing logarithmic terms pop up in the regime
soft limit (squared amplitude)
collinear limit (squared amplitude)
These new terms vanish for , so that the standard factorization of soft and collinear singularities is preserved as
Exact treatment of quark masses
e.g. including top and bottom quarks at relative order
⇠ (mb/mH)4 ln4(m2b/p2
t )
⇠ (mbmt)2/m4
H ln2(m2b/p2
t ) ln2(m2t /p2
t )
non-factorizing terms completely cancel in the top-bottom interference
O(↵s)
interference terms survive and give a dominant contribution
pt ! 0
Masses and soft factorisationTop and bottom loops have also a different behaviour with respect to factorisation of soft emissions in the region
pt ⌧ mH ⌧ mt mb ⌧ pt ⌧ mH
H
W+
W�
W+
W�
H
pt
pt
pt,veto = 25 � 30 GeV
Top loop: Bottom loop:
Soft gluons cannot resolve the top loop factorisation OK)
Soft gluons can resolve a bottom loop factorisation breaking?)
mbmt
m2b << p2
t << m2H
mb, mt
pt mb
No factorization breaking ! Just a larger remainder...
Gluon fusion: Choosing the resummation scaleI bad high pT matching for large QI due to unitarity: cross section will even become negativeI pragmatic way to determine Q: [Harlander, Mantler, MW ’14]
require that cross section remains positive for Q = 2Q0
0
0.5
1
1.5
2
100 150 200 250 300 350 400
(dσ
res /
dpT)
/ (dσ
fo/d
p T)
pT [GeV]
Qres = 94 GeVQres = 96 GeVQres = 98 GeV
Qres = 100 GeVQres = 102 GeV
0
0.5
1
1.5
2
100 150 200 250 300
(d�r
es/d
p T) /
(d�f
o /dp
T)
pT [GeV]
Qres = 42 GeVQres = 44 GeVQres = 46 GeVQres = 48 GeVQres = 50 GeV
0
0.5
1
1.5
2
100 150 200 250 300 350
(d�r
es/d
p T) /
(d�f
o /dp
T)
pT [GeV]
Qres = 64 GeVQres = 66 GeVQres = 68 GeVQres = 70 GeVQres = 72 GeV
high pT matching → Qt = 49GeV, Qb = 23GeV, Qtb = 34GeV
finite terms (for pvetoT ) → Qt ∼ 60GeV, Qb ≡ Qtb ∼ 35GeV
soft/collinear approx (10%) → Qt ∼ 55GeV, Qb ∼ 25GeV
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 11
top bottom interference
Gluon fusion: Choosing the resummation scaleI bad high pT matching for large QI due to unitarity: cross section will even become negativeI pragmatic way to determine Q: [Harlander, Mantler, MW ’14]
require that cross section remains positive for Q = 2Q0
0
0.5
1
1.5
2
100 150 200 250 300 350 400
(dσ
res /
dpT)
/ (dσ
fo/d
p T)
pT [GeV]
Qres = 94 GeVQres = 96 GeVQres = 98 GeV
Qres = 100 GeVQres = 102 GeV
0
0.5
1
1.5
2
100 150 200 250 300
(d�r
es/d
p T) /
(d�f
o /dp
T)
pT [GeV]
Qres = 42 GeVQres = 44 GeVQres = 46 GeVQres = 48 GeVQres = 50 GeV
0
0.5
1
1.5
2
100 150 200 250 300 350
(d�r
es/d
p T) /
(d�f
o /dp
T)
pT [GeV]
Qres = 64 GeVQres = 66 GeVQres = 68 GeVQres = 70 GeVQres = 72 GeV
high pT matching → Qt = 49GeV, Qb = 23GeV, Qtb = 34GeVfinite terms (for pveto
T ) → Qt ∼ 60GeV, Qb ≡ Qtb ∼ 35GeVsoft/collinear approx (10%) → Qt ∼ 55GeV, Qb ∼ 25GeVM. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 11
top bottom interference
1. size of finite termsI considered for pjet
T ,veto efficiencies[Banfi, Monni, Zanderighi ’13]
finite terms ≤ 50% → Qt ∼ 60GeV, Qb ≡ Qtb ∼ 35GeV
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 11
0
0.2
0.4
0.6
0.8
1
1 10 100
ε rem
aind
er(p
t,vet
o)/ε
rem
aind
er(p
t,vet
o=∞
)
pt,veto [GeV]
mH = 125 GeV
mt = 173.5 GeV; mb = 4.65 GeV
| t |2
| b |2+2 Re[b*⋅ t]| t+b |2
2. validity of collinear approximationI at matrixelement level for pT Higgs→more in Alessandro’s talk
[Bagnaschi, Vicini]
max 10% deviation → Qt ∼ 55GeV, Qb ∼ 25GeV
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 10 / 11
Alessandro Vicini - University of Milano CERN, December 16th 2013
Collinear approximation of the full amplitude summed over helicities
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
|M(m)|2 =X
�1,�2,�3=±1
|M�1,�2,�3(m)|2 =X
�1,�2,�3=±1
|M�1,�2,�3
div (m)/pH? + M�1,�2,�3
reg (m)|2
C(pH? ) =
|Mexact(pH? )|2
|Mdiv(pH? )/pH
? |2
sum over helicities of the amplitudes evaluated with:
only top, only bottom, top+bottom
Alessandro Vicini - University of Milano CERN, December 16th 2013
Collinear approximation of the full amplitude summed over helicities
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
50 100 150 200 250 300ptH HGeVL
0.8
1.0
1.2
1.4
C
|M(m)|2 =X
�1,�2,�3=±1
|M�1,�2,�3(m)|2 =X
�1,�2,�3=±1
|M�1,�2,�3
div (m)/pH? + M�1,�2,�3
reg (m)|2
C(pH? ) =
|Mexact(pH? )|2
|Mdiv(pH? )/pH
? |2
sum over helicities of the amplitudes evaluated with:
only top, only bottom, top+bottom
t-only b-only
Gluon Fusion: ResultsNLO+NLL distribution in the SM:[Harlander, Mantler, MW ’14][
dσdp2
T
]NLO+NLL
=
[dσ
dp2T
]NLO−[
dσ(res)dp2
T
]NLO
+
[dσ(res)dp2
T
]NLL
10-4
10-3
10-2
10-1
100
0 50 100 150 200 250 300
dσ/d
p T [p
b/G
eV]
pT [GeV]
SM, mH = 125.6 GeV, pp @ 13 TeV
SMf.o.
0.7
0.8
0.9
1
1.1
1.2
1.3
0 50 100 150 200 250 300
(dσ
x /dp
T) /
(dσ
htl /d
p T)
pT [GeV]
pp @ 13 TeV
b+tt
M. Wiesemann (University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 11